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We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent…
We calculate analytically the transmission and reflection amplitudes for waves incident on a rotating black hole in d=4, analytically continued to asymptotically large, nearly imaginary frequency. These amplitudes determine the asymptotic…
The separation of acoustic and vortical fluctuations in compressible turbulence becomes ambiguous in thermodynamically inhomogeneous media, where refraction by entropy gradients and shocks can be misclassified as solenoidal content by…
We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasistatic approximation. Our theoretical model gives us access to both the longitudinally and…
This paper is devoted to Maxwell modes in three-dimensional bounded electromagnetic cavities that have the form of a product of lower dimensional domains in some system of coordinates. The boundary conditions are those of the perfectly…
The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in…
Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…
We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU(2) method, we obtain analytic formulae that give excellent…
We consider the interaction of two level ultracold atoms resonant with a sinusoidal mode of the electromagnetic field in a high Q cavity. We found that well resolved resonances appear in the transmission coefficients even for actual…
The coalescence of two black holes generates gravitational waves that carry detailed information about the properties of those black holes and their binary configuration. The final coalescence cycles are in the form of a {\it ringdown}: a…
The external-Q factor of a resonant mode of a cavity represents the strength of the electromagnetic coupling between this resonant mode and the transmission mode of a waveguide coupled to the cavity. In this paper, we derive formulas to…
We are interested in the Helmholtz equation in a junction of two periodic half-spaces. When the overall medium is periodic in the direction of the interface, Fliss and Joly (2019) proposed a method which consists in applying a partial…
We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with…
The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and…
Taking the horizon surface of the black hole as a compact membrane and solving the oscillation equation of this membrane by Klein-Gordon equation, we derive the frequencies of oscillation modes of the horizon surface, which are proportional…
The resonator is one of the main building blocks of a plethora of photonic and microwave devices from nanolasers to compact biosensors and magnetic resonance scanners. The symmetry of the resonators is tightly related to their mode…
The cavity perturbation technique is an extremely powerful method for measuring the electrodynamic response of a material in the millimeter- and sub-millimeter spectral range (10 GHz to 1 THz), particularly in the case of…
We present the mathematical theory of one-dimensional infinitely periodic chains of subwavelength resonators. We analyse both Hermitian and non-Hermitian systems. Subwavelength resonances and associated modes can be accurately predicted by…
The confinement properties of the open structure formed crossing a circular waveguide perpendicular to a parallel-plate waveguide are discussed, highlighting the fundamental differences with respect to the common high-frequency resonators.…